Question

Suppose the S&R index is 1000 and the dividend yield is zero. The continuously compounded borrowing rate is 5% while the continuously compounded lending rate is 4.5%. The maturity of the forward contract is 6 months.

(a) Suppose when you buy or sell the index, there is a transaction cost of $1 at t=0. There is also a transaction cost of $2 if you take a long or short forward position at t=0. There are no transaction costs on the maturity date. The futures price is 1026. Which of the statement is true?

A. You can do cash-and-carry arbitrage

B. You can do reverse cash-and-carry arbitrage

C. You can do both cash-and-carry and reverse cash-and-carry arbitrage

D. You cannot arbitrage

(b) Following part (a), what is the non-arbitrage upper bound of the forward price?

Answer 1

Answer is B

We can do REVERSE CASH AND CARRY ARBITRAGE

In that we need to :

1. Buy forward

2. Short sell asset

3. Invest that money

Forward price = 1026

Long Forward contract @1026

Transaction fee = 2

Short sell index and get 1000

Transaction fee = 1

Invest = 1000

interest = 4.5%

Amount after 1 year = 1000 * exp^0.045 = 1046.027

Total = 1046.027 - 2 - 1 = 1043.027

Settle the long position by paying 1026

So Profit = 1043.027 - 1026 = 17.027

Buy spot asset

short sell forward